One cannot hear the winding number

2006/12/07 by Jean Bourgain, Gady Kozma, Bourgain, Jean +1 · 1 citation
Mathematics · #42A16 (primary) #42A61 (secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42A16 #msc:42A61

paper · pdf · doi:10.48550/arxiv.math/0612192

19 pages, 1 figure

arxiv created 2006/12/07 · arxiv updated 2009/12/01

Abstract

We construct an example of two continuous maps f and g of the circle to itself with the same absolute value of the Fourier transform but with different winding numbers, answering a question of Brezis.

Cited by

• Nonexistence of universal Fourier summation formulas for the degree below the Hölder threshold α=1/3

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